29 citations · 77 across the 13 of their papers we have counts for
15 papers
Multipreconditioning with directional sweeping methods for high-frequency Helmholtz problems
Niall Bootland, Tyrone Rees
We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present…
A robust and adaptive GenEO-type domain decomposition preconditioner for problems in three-dimensional general topologies
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-ty…
Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation
Niall Bootland, Sahar Borzooei, Victorita Dolean +1
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improv…
Can DtN and GenEO coarse spaces be sufficiently robust for heterogeneous Helmholtz problems?
Niall Bootland, Victorita Dolean
Numerical solution of heterogeneous Helmholtz problems presents various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robust…
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and non-self-adjoint problems
Niall Bootland, Victorita Dolean, Ivan G. Graham +2
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for computing an operator-dependent spectral coarse space to be combined with local solves on subdomains to for…
Inexact subdomain solves using deflated GMRES for Helmholtz problems
Niall Bootland, Vandana Dwarka, Pierre Jolivet +2
We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholt…
GenEO coarse spaces for heterogeneous indefinite elliptic problems
Niall Bootland, Victorita Dolean, Ivan G. Graham +2
Motivated by recent work on coarse spaces for Helmholtz problems, we provide in this paper a comparative study on the use of spectral coarse spaces of GenEO type for heterogeneous…
Several ways to achieve robustness when solving wave propagation problems
Niall Bootland, Victorita Dolean, Pierre Jolivet +3
Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillator…
Two-level DDM preconditioners for positive Maxwell equations
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type eq…
A comparison of coarse spaces for Helmholtz problems in the high frequency regime
Niall Bootland, Victorita Dolean, Pierre Jolivet +1
Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high…
Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices
Niall Bootland, Victorita Dolean, Alexandros Kyriakis +1
In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helm…
Multipreconditioning with application to two-phase incompressible Navier-Stokes flow
Niall Bootland, Andrew Wathen
We consider the use of multipreconditioning to solve linear systems when more than one preconditioner is available but the optimal choice is not known. In particular, we consider a…
On the Dirichlet-to-Neumann coarse space for solving the Helmholtz problem using domain decomposition
Niall Bootland, Victorita Dolean
We examine the use of the Dirichlet-to-Neumann coarse space within an additive Schwarz method to solve the Helmholtz equation in 2D. In particular, we focus on the selection of how…
Preconditioners for Two-Phase Incompressible Navier-Stokes Flow
Niall Bootland, Alistair Bentley, Christopher Kees +1
We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using m…
Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators
Hadrien Montanelli, Niall Bootland
Dozens of exponential integration formulas have been proposed for the high-accuracy solution of stiff PDEs such as the Allen-Cahn, Korteweg-de Vries and Ginzburg-Landau equations.…